Scholarlink

<p>Let <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\Omega (n, k)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>,</mo> <mi>k</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> be the set of <i>k</i>-dimensional <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\((-1, 1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-matrices of order <i>n</i>. A new formula for computing the multidimensional permanents of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\((-1, 1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-matrices is provided. As an application of this formula, the divisibility of the permanent of a multidimensional <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\((-1, 1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> matrix by certain powers of 2 is established. Bibliography: 16 titles.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

DIVISIBILITY OF THE PERMANENTS OF MULTIDIMENSIONAL \((-1, 1)\)-MATRICES BY POWERS OF 2

  • 期刊论文

  • 发表日期：

    2026年5月19日

查看全文
  • T. A. Asmus,
  • A. E. Guterman

摘要

Let \(\Omega (n, k)\) Ω ( n , k ) be the set of k-dimensional \((-1, 1)\) ( - 1 , 1 ) -matrices of order n. A new formula for computing the multidimensional permanents of \((-1, 1)\) ( - 1 , 1 ) -matrices is provided. As an application of this formula, the divisibility of the permanent of a multidimensional \((-1, 1)\) ( - 1 , 1 ) matrix by certain powers of 2 is established. Bibliography: 16 titles.